Statistica Sinica 25 (2015), 1477-1502
Abstract: This paper is dedicated to the study of an estimator of the generalized Hoeffding decomposition. We build an estimator using an empirical Gram-Schmidt approach and derive a consistency rate in a large dimensional setting. We then apply a greedy algorithm with these previous estimators to a sensitivity analysis. We also establish the consistency of this L2-boosting under sparsity assumptions of the signal to be analyzed. The paper concludes with numerical experiments that demonstrate the low computational cost of our method, as well as its efficiency on the standard benchmark of sensitivity analysis.
Key words and phrases: L2-boosting, convergence, dependent variables, generalized ANOVA decomposition, sensitivity analysis.